# Black holes, without the math > A place even light can't leave, and how we know it's really out there. A free course from Learnfold. 6 lessons, 20–30 min. Web: https://learnfold.app/learn/black-holes/ ## What you'll learn Explain in plain words what a black hole is, how one forms, what falling in would do to you, and how astronomers know they exist. ## Before you start No physics or math needed. If you've ever thrown a ball in the air, you have the background. ## Outline ### Chapter 1: What a black hole is Squeeze enough mass into a small enough space and light can't get out. See how nature does it, and what crossing the edge would do to you. 1. [A place light can't leave](https://learnfold.app/learn/black-holes/escape/): Escape velocity, and what happens when it passes the speed of light. 2. [How a star becomes a black hole](https://learnfold.app/learn/black-holes/collapse/): Why heavy stars collapse, why the Sun won't, and the giants at the centers of galaxies. 3. [What falling in would be like](https://learnfold.app/learn/black-holes/falling-in/): The event horizon, spaghettification, and why a bigger black hole is gentler at the edge. ### Chapter 2: Seen and unseen Watch time slow near a black hole, see how astronomers found things that give off no light, and meet the questions nobody has answered. 4. [Clocks that run slow](https://learnfold.app/learn/black-holes/slow-time/): Gravity slows time, near Earth and enormously near a black hole. 5. [How we see something black](https://learnfold.app/learn/black-holes/seeing/): Orbiting stars, glowing disks, gravitational waves, and the first pictures. 6. [What nobody knows yet](https://learnfold.app/learn/black-holes/unknowns/): Hawking radiation, the information paradox, and where physics runs out. ## Lessons ## 1. A place light can't leave Throw a ball straight up and it comes back down. Throw it harder and it climbs higher before it falls. Somewhere there is a speed where it never comes back. Earth's gravity keeps slowing it, but never enough to turn it around. That speed is called escape velocity, and for Earth it's roughly 11 kilometers per second, about 40,000 km/h. That's why rockets are mostly fuel. ### Squeeze it and the speed goes up Escape velocity depends on two things. One is how much mass is pulling on you, and the other is how close you are to its center. From the surface of the Sun, which is far heavier than Earth, you'd need roughly 600 kilometers per second. Now keep the mass the same and shrink the size. You're standing closer to all that mass, so escape gets harder. Squeeze far enough and escape velocity passes the speed of light, about 300,000 kilometers per second. Nothing can go faster than light, so nothing gets out. Not even light. That's a black hole. It isn't a hole and it isn't a thing made of black stuff. It's a region of space where gravity has won completely. Choose outside, at the horizon, then inside. The blue wedge shows possible radial futures, with light on its edges; it does not show light slowing down locally. ### An old idea that turned out real In 1783 an English clergyman named John Michell made this exact argument with Newton's physics. He imagined "dark stars" so heavy that their own light would fall back. It was a clever guess, and nobody could check it. The real version came from Einstein, who described gravity as the bending of space and time. Within weeks of his 1915 theory, a German astronomer named Karl Schwarzschild, serving on the Russian front in World War I, sent him an exact solution for the space around a ball of mass. Hidden in it was a boundary that nothing could come back from. Schwarzschild died a few months later. The name "black hole" came decades after that, made popular by the physicist John Wheeler in 1967. ### How small is small enough? The size of that boundary depends only on mass. Double the mass and it doubles in size. Pick an object below and squeeze it. Pick an object and tap Squeeze, then Reset. The picture is not to scale; the text gives the size needed for that mass. Earth would need to fit in a marble. The Sun would need to shrink to a ball you could walk across in a little over an hour. Nothing in your daily life comes close to that kind of squeezing, which is why black holes sound so strange. Nature can do it, though, and the next lesson shows how. ### They don't suck One myth to drop now. A black hole doesn't vacuum up everything around it. From far away, it pulls exactly like any other object with the same mass. If the Sun were swapped for a black hole of equal mass, Earth would keep orbiting on the same path. It would get very cold and very dark, but it wouldn't fall in. ### Rabbit holes > Why can't anything go faster than light, even in principle? > If the Sun turned into a black hole tomorrow, what would actually happen on Earth, hour by hour? > How did John Michell work out dark stars with only Newton's physics? Read online: https://learnfold.app/learn/black-holes/escape/ ## 2. How a star becomes a black hole A star is a long tug of war. Gravity pulls all of its gas inward. Nuclear fusion in the core, the same process behind a hydrogen bomb, heats the gas and pushes outward. For most of a star's life the two sides balance. The Sun has held steady for about 4.6 billion years and has roughly 5 billion to go. When the fuel runs out, the push stops. Gravity wins. What's left depends mostly on how heavy the star was to begin with. | Star's mass at birth | What it leaves behind | | --- | --- | | Up to about 8 Suns | A white dwarf, a cooling ember about the size of Earth | | About 8 to 20 Suns | Usually a neutron star, about the width of a city | | More than about 20 Suns | Often a black hole | Treat those cutoffs as rough. They depend on how much gas a star blows away during its life, what it's made of, and how fast it spins. Astronomers still argue about the exact lines. ### The last second of a giant A heavy star fuses lighter elements into heavier ones, layer by layer, until its core is iron. Fusing iron doesn't release energy, so the core suddenly has nothing holding it up. It collapses in a fraction of a second. Often the outer layers blast away in a supernova, an explosion that can outshine a whole galaxy for weeks. What happens to the core depends on its weight. Up to roughly 2 or 3 times the Sun's mass, the core can stop as a neutron star, so dense that a teaspoon of it would weigh billions of tons. Heavier than that, and nothing we know of can hold it up. It keeps falling inward, past the size from the last lesson, and becomes a black hole. Play or scrub the collapse. Follow the core as it shrinks through the marked radius; the figure leaves out the outer star and any supernova. These stellar black holes usually weigh somewhere between 5 and a few dozen Suns. Astronomers estimate our galaxy holds millions of them, nearly all invisible because nothing is falling into them. Our own Sun is far too light for any of this. In a few billion years it will swell into a red giant, shed its outer layers, and settle down as a white dwarf. It will never become a black hole. ### The giants in the middle There's a second kind, and it's much bigger. Supermassive black holes weigh millions to billions of Suns and sit at the centers of most large galaxies. Ours, called Sagittarius A*, is about 4 million Suns and roughly 26,000 light-years away. The one at the center of the galaxy M87 is about 6.5 billion Suns. How they got so big is an open question. Swallowing gas and merging with other black holes for billions of years explains part of it. But telescopes keep finding giant ones that already existed less than a billion years after the Big Bang, which seems too early to grow that way. Maybe some started huge, from enormous gas clouds collapsing all at once. Nobody knows yet. ### Rabbit holes > What actually stops a white dwarf or a neutron star from collapsing any further? > How could supermassive black holes grow so big so early in the universe? > What's the nearest known black hole to Earth, and should I worry about it? Read online: https://learnfold.app/learn/black-holes/collapse/ ## 3. What falling in would be like Nobody has fallen into a black hole and reported back, and nobody ever will. Everything on this page comes from Einstein's theory, which has passed every test we've given it outside black holes, followed all the way to its conclusions. Keep that in mind. It's a very good guess, not a travel report. ### The edge isn't a wall The boundary you can't come back from is called the event horizon. It's not a surface. There's nothing there to hit, no glowing shell, no sign. It's a point of no return, like the spot on a river above a waterfall where the current gets faster than you can swim. You can drift past it without noticing, and after that, every direction you could possibly move leads further in. ### Stretched like spaghetti Gravity gets stronger the closer you are. Fall feet first and your feet are a little closer than your head, so they're pulled a little harder. On Earth the difference is far too small to feel. The same effect raises the ocean tides, because the Moon pulls harder on the near side of Earth than the far side. Near a small black hole that difference becomes brutal. Take one about 10 times the Sun's mass, with a horizon roughly 60 kilometers across. Long before you reached the horizon, perhaps a thousand kilometers out, the pull on your feet would outstrip the pull on your head so badly that you'd be stretched long and thin and torn apart. Physicists really do call this spaghettification. This part isn't only theory. Astronomers have watched whole stars wander too close to supermassive black holes and get shredded. The flare of light from a star being pulled apart can last for months. ### Bigger is gentler Here's the surprise. A supermassive black hole is kinder at the edge than a small one. The stretch depends on how quickly gravity changes over the length of your body. A huge black hole has a huge horizon, and at that distance from the center, gravity changes very slowly over 2 meters. At the horizon of Sagittarius A*, the stretch would be too gentle to notice. You'd cross the point of no return in one piece, maybe without realizing it. Play or scrub toward the horizon, then switch masses. At a fixed number of horizon radii, tidal strength falls with the square of the black hole mass. Your luck runs out later. Inside, the theory says you're carried toward the center, and the stretching grows until it tears you apart there too. For our galaxy's black hole, the whole trip from horizon to center would take at most about a minute by your own watch. For the far heavier one in M87, more like a day. ### What's at the bottom? The math says all the mass ends up crushed into a single point of infinite density, called a singularity. Most physicists don't believe that's literally true. When a theory starts producing infinities, it usually means the theory has stopped working. Something else takes over at the center, probably a theory that joins gravity with quantum physics. Nobody has one that works yet. ### Rabbit holes > If I fell into a supermassive black hole, what would I see if I looked back out? > Why does a bigger black hole stretch you less at its edge? Walk me through it without equations. > What does it look like when a black hole tears a star apart? Read online: https://learnfold.app/learn/black-holes/falling-in/ ## 4. Clocks that run slow Einstein's theory makes a strange claim. Gravity slows time. A clock closer to a heavy object ticks more slowly than one farther away. This isn't a flaw in the clocks. Everything slows together, atoms, heartbeats, the aging of cells. Whoever is near the heavy object feels perfectly normal. Only when two people compare watches afterward does the difference show. ### It happens here too The effect is real near Earth, just tiny. GPS satellites orbit about 20,000 kilometers up, where gravity is weaker, so their clocks run fast. Their speed slows them a little, but the net result is a gain of roughly 38 millionths of a second a day. Engineers adjust for it. If they didn't, the position on your phone's map would drift by kilometers within a day. In 2010, researchers in the United States lifted one extremely precise clock about a third of a meter higher than another. The higher clock ran measurably faster. By the same logic, over a lifetime your head ages a few hundred billionths of a second more than your feet. ### Near a black hole, it's enormous Close to a black hole, the slowing stops being a rounding error. Here's how fast a clock would tick compared with one far away, if it could hover in place near a black hole that isn't spinning. Distances are measured from the center, in multiples of the horizon's radius. | Where the clock hovers | How fast it ticks | | --- | --- | | 10 times the horizon radius | About 95% speed | | 2 times | About 70% | | 1.1 times | About 30% | | 1.01 times | About 10% | | At the horizon | Stopped, as seen from far away | Hovering that close would take an impossibly powerful rocket. But the numbers show the shape of it. The last stretch before the horizon is where time really drags. Choose a radius and press Play to compare elapsed time. Each clock feels normal beside itself; the difference appears when their readings are compared. ### Two views of one fall Say you fall in while a friend watches from a safe distance. You'd notice nothing odd about your own watch, and you'd cross the horizon without any pause. Your friend sees something else. You seem to move more and more slowly as you approach the edge. Your light gets redder and dimmer and finally fades out. They never quite see you cross. Both accounts are correct for the person telling them. That's the part that takes a while to sit comfortably. The film Interstellar has a planet where one hour equals seven years back home. Its science adviser, the physicist Kip Thorne, worked out that this needs a giant black hole spinning almost as fast as physics allows. Possible on paper. Nobody has found one like it. ### Caught in the act In 2018 astronomers watched a star called S2 swing close past Sagittarius A*, at roughly 120 times the distance from Earth to the Sun. As it passed, its light came out slightly stretched toward red, by the amount Einstein's theory predicts. That stretch is slowed time, seen through light. It's the same effect, measured near a real black hole. ### Rabbit holes > Could I use a black hole as a one-way time machine into the future? > Why does gravity slow time at all? Give me an intuition, not an equation. > How exactly do GPS satellites correct for relativity? Read online: https://learnfold.app/learn/black-holes/slow-time/ ## 5. How we see something black You can't see a black hole. You can see what it does to everything around it. Astronomers have found four ways to catch one. ### Stars on impossible orbits Starting in the 1990s, two teams spent decades tracking stars near the center of our galaxy, whipping around something invisible. One star, S2, completes a lap every 16 years or so. To explain those orbits you need about 4 million Suns' worth of mass packed into a region not much bigger than our solar system. Nothing but a black hole fits. Andrea Ghez and Reinhard Genzel each won a share of the 2020 Nobel Prize in Physics for that work. ### Gas that glows before it vanishes Gas falling toward a black hole doesn't drop straight in. It swirls into a flat disk, rubbing against itself and heating to millions of degrees, hot enough to shine in X-rays. Cygnus X-1, an X-ray source spotted in 1964, became the first widely accepted black hole in the early 1970s. Stephen Hawking famously bet that it wasn't one, then conceded in 1990. The supermassive ones can do this on a grand scale. A quasar is a giant black hole feeding so fast that its disk outshines the hundreds of billions of stars in its galaxy. Something that gives off no light of its own ends up among the brightest things in the universe. Drag sideways to tilt this schematic disk from face-on toward edge-on. Real images also bend light around the hole, so their bright rings are not simple views of this disk. ### Ripples in space On September 14, 2015, two detectors called LIGO, one in Washington State and one in Louisiana, felt a faint wobble. Each detector has two arms 4 kilometers long, and their lengths changed by a tiny fraction of the width of a proton. The signal lasted under a second. It came from two black holes, roughly 36 and 29 times the Sun's mass, spiraling together and merging about 1.3 billion light-years away. In that last instant they turned about three Suns' worth of mass into ripples in space itself, called gravitational waves. It was the first direct proof that black holes come in pairs and merge. Three of its leaders won the 2017 Nobel Prize, and detectors have since recorded hundreds of mergers. ### The first pictures In April 2019, the Event Horizon Telescope released the first image of a black hole. It shows a glowing ring around a dark center, at the heart of the galaxy M87, about 55 million light-years away. The team linked radio telescopes across the world to work like one telescope the size of Earth, and separate teams checked the processing. The dark center is called the shadow. It isn't the horizon itself. Light bends around the black hole, so the shadow looks about two and a half times wider than the horizon. In May 2022 they released a picture of Sagittarius A*. That one was harder. It's far smaller than the one in M87, so gas circles it in minutes instead of days, and the view kept changing while they recorded it. Both images come from observations made in 2017. ### What this does and doesn't prove Everything here is observed, and it all matches Einstein's description of black holes. None of it shows us the inside. The horizon itself is inferred from how everything around it behaves. That's a strong inference, but still one step removed. ### Rabbit holes > How can radio dishes on different continents act like one giant telescope? > What did Stephen Hawking lose when he bet against Cygnus X-1? > How did LIGO measure a change smaller than a proton without being fooled by trucks and earthquakes? Read online: https://learnfold.app/learn/black-holes/seeing/ ## 6. What nobody knows yet So far you've seen two kinds of claims. Some are observed, such as stars orbiting nothing visible, X-ray disks, gravitational waves, and the images. Others are strong theory, such as what the horizon is like and what falling in would feel like. This lesson is the third kind, where the best physicists alive disagree. ### Black holes might not be black In 1974 Stephen Hawking combined Einstein's gravity with quantum physics, the rules for very small things, and got a shock. Black holes should glow very faintly and slowly lose mass. This is now called Hawking radiation. The usual picture involves pairs of particles appearing near the horizon, with one escaping. Hawking himself said that's a rough cartoon of the real math. "Faintly" is an understatement. A black hole with the Sun's mass would have a temperature of about 60 billionths of a degree above absolute zero. Empty space is warmer than that. It still glows at about 2.7 degrees above absolute zero, left over from the Big Bang. So real black holes today take in more energy than they give off. Even once the universe cools down, a black hole like that would take around 10 to the power of 67 years to evaporate. The universe is about 14 billion years old. Hawking radiation has never been detected from a real black hole. Lab experiments using sound in ultracold gases have produced a lookalike effect. Most physicists expect it's real, because it comes from two theories that have each been tested very well. Expecting isn't the same as seeing. ### Where does the information go? Physics has a deep rule. Information is never truly destroyed. Burn a book and, in principle, the smoke, ash, and heat still carry every word, scrambled beyond any practical recovery but still there. Now throw the book into a black hole and wait for it to evaporate. Hawking's calculation says what comes out is a random glow that depends only on the black hole's mass, spin, and charge. Throw in a dictionary instead and you'd get the same glow. The information seems to vanish. That's the information paradox. For decades Hawking argued the information really is lost. In 2004 he changed his mind and conceded a bet to the physicist John Preskill, paying him with a baseball encyclopedia. Since 2019, new calculations have suggested how information could leak back out with the radiation, and many physicists now lean that way. Nobody has shown exactly how it happens. ### Where things stand | Claim | Status | | --- | --- | | Black holes exist, with the masses we measure | Observed | | Black holes shred stars that come too close | Observed | | Time slows near them | Observed in small amounts | | Event horizons | Strongly supported, never seen directly | | Hawking radiation | Predicted, not detected | | What's at the center | Unknown | | Whether information escapes | Unknown, actively argued | Pick a claim to inspect its evidence. A successful prediction and a direct observation answer different questions. Black holes are where Einstein's gravity and quantum physics are both needed at once, and the two don't fit together yet. That makes them the best natural laboratory we have for the biggest unsolved problem in physics. ### Rabbit holes > Why do physicists care so much about information never being destroyed? > Could a tiny black hole left over from the early universe be evaporating somewhere we could see it? > What would a theory of quantum gravity need to explain about black holes? Read online: https://learnfold.app/learn/black-holes/unknowns/ --- Read this course in the Learnfold app to ask about any sentence, follow a question into a new lesson, or have it rebuilt around what you already know: https://apps.apple.com/us/app/learnfold/id6794672797